What is (\partial)/(\partial x)(e^tx+1) ?

The answer to (\partial)/(\partial x)(e^tx+1) is e^t

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(\partial)/(\partial x)(e^tx+1)

\frac{\partial}{\partial x} (e^{t} x + 1)

e^{t}

Solution steps

\frac{\partial}{\partial x} (e^{t} x + 1)

Treat

t

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (e^{t} x) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (e^{t} x) = e^{t}

\frac{\partial}{\partial x} (1) = 0

= e^{t} + 0

Simplify

= e^{t}

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What is (\partial)/(\partial x)(e^tx+1) ?
The answer to (\partial)/(\partial x)(e^tx+1) is e^t